I am not an engineer, but long ago was an electronics technician, so use this response with caution and common sense. There are a couple of techniques to desolder the RF shield. First, I am assuming the shield or whatever you want to refer to the large housing you've referred to above has several pins inserted all the way through the PCB and it might have some larger tabs for support all soldered to the PCB on the opposite side.
First, yes you can and should solder this RF shield back on after working 'under-the-hood' so to speak - if it is and probably is an RF shield it will help eliminate or reduce incoming and outgoing RF signals which has an impact on the signal to noise ratio of the device (note: I am not an RF engineer, but common sense would suggest to replace any shield to it's original configuration).
To de-solder and solder this back you should have or obtain the following items:
A soldering iron.
A desoldering braid. This is finely woven or braider copper wire that, once heated, will allow melted solder to wick up the braid and away from the PCB board and away from the components.
Desoldering Bulb. This is a "sucking tool" to pull the melted solder away from the PCB board.
- Soldering Flux
- 99.95% alcohol - here: http://www.mgchemicals.com/products/cleaners/electronic-cleaners/isopropyl-alcohol-824/
If you have a soldering iron, you can "de-wet?" the solder - meaning making it just hot enough to melt the existing solder and wick it away from the pins and pad. (this is probably not the right definition or worded properly, but its the process of dewetting, nonetheless from everything I can recall.
At the same time, you should be heating the braid and try to get all the melted solder to wick up the braid. One thing to mention: This is a technique that needs to be practiced prior to working on the actual circuit board to really get the technique of getting the solder to melt and the braid to heat up properly. and I think the best way to do it is to get a bit of solder flux on the braid then place the braid on the solder joint (the actual soldered pad and the pin) then touch the soldering iron tip to the braid. The heat should transfer through the braid, "boil' the flux and then melt the solder, in turn causing the solder to wick up the braid. (Here's a video: https://www.youtube.com/watch?v=TItFOKj4Bio, but be careful not to hold the tip of the iron too long, or the rocking motion the youtuber is using with the braid might cause the pad (trace) to actually rip off the pcb material. (there's a fix to that too, but this is a long response already :))
By the way, the "Desoldering bulb" might assist in pulling way excessive solder from the sides (bigger amounts of solder like on the tabs mentioned above).
And once you are finished, clean the flux away with the alcohol a few times (even if you think it's cleaned off, do it one more time, using a cotton swab, this will help reduce the chance the flux continues to react over time with the board and could cause all kinds of issues with the looks and the functionality of the solder joints and even the traces.